I Tavi

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I <strong>Tavi</strong> 52 39 A punqtidan B punqtisaken gaemarTa tivi. 2 sT 40 wT-is Semdeg mis Sesaxvedrad B punqtidan gamovida kateri, romelic Sexvda tivs B punqtidan 27 km-is daSorebiT. ipoveT tivis siCqare, Tu kateris siCqare mdgar wyalSi aris 12 km/sT da manZili A da B punqtebs Soris 44 km-ia. 40 avtoturistma A da B punqtebs Soris manZili, romelic 400 km-ia, raRac saSualo siCqariT gaiara. ukan dabrunebisas 2 saaTis ganmavlobaSiigiimavesiCqariTmidioda,SemdegkisiCqare10km/sT-iT gazarda, ris gamoc A punqtSi dabrunebaze 40 wuTiT naklebi dro daxarja,vidreA-danB-SiCasvlaze.radrodauxarjavsavtoturists B-dan A-Si dabrunebaze? 41 motociklistma erTi qalaqidan meoreSi Casvlas 4 sT moandoma. ukan dabrunebisas pirveli 100 km gaiara imave siCqariT, Semdeg siCqare Seamcira 10 km/sT-iT da amitom ukan dabrunebas moandoma 30 wuTiT meti dro. ipoveT manZili qalaqebs Soris. 42 A da B qalaqebidan erTdroulad, erTmaneTis Sesaxvedrad gamosuli ori avtomanqana erTmaneTs Sexvda 5 saaTis Semdeg. A-dan gamosuli avtomanqanis siCqare 10 km/sT-iT naklebia meore avtomanqanis siCqareze. pirveli avtomanqana A-dan 4 sT 30 wT-iT adre rom gamosuliyo, maSin isini Sexvdebodnen erTmaneTs B-dan 150 km-is daSorebiT. ipoveT manZili A da B qalaqebs Soris. 43 M navsadguridan N navsadguramde manZils mdinaris dinebis mimarTulebiT kateri gadis 6 saaTSi. erTxel M sadguridan gamosuli kateri, roca N navsadguramde 40 km iyo darCenili, isev ukan M navsadgurSi dabrunda, am gzis gavlas ki 9 saaTi moandoma. ipoveT kateris siCqare mdgar wyalSi, Tu mdinaris dinebis siCqare 2 km/sT-ia. 44 navi 9 saaTze gavida A punqtidan mdinaris dinebis sawinaaRmdego mimarTulebiT da mivida B punqtSi. 2 saaTis Semdeg navi ukan gamobrunda da A punqtSi dabrunda 19sT da 20wT-ze. romel saaTze mivida navi B punqtSi, Tu manZili A da B punqtebs Soris 60km-ia, mdinaris dinebis siCqare ki 3km/sT-ia. 45 ori velosipedisti erTdroulad gamodis erTmaneTis Sesaxvedrad ori A da B punqtidan, romelTa Soris manZili 28 km-ia da erTi saa- Tis Semdeg xvdebian erTmaneTs. isini SeuCereblad ganagrZoben gzas imave siCqariT da pirveli B punqtSi midis 35 wT-iT ufro adre, vidre meore A punqtSi. ipoveT TiToeuli velosipedistis siCqare. 46 ori A da B punqtidan, romelTa Soris manZili 24 km-ia, erTsa da imave dros erTmaneTis Sesaxvedrad ori avtomobili gaigzavna. maTi Sexvedris Semdeg A-dan gamosuli avtomobili B punqtSi midis 16 wT-Si,
xolo meore avtomobili 4 wuTSi midis A punqtSi. ipoveT TiToeuli avtomobilis siCqare. 47 aerodromidan erTdroulad ori TviTmfrinavi gafrinda: erTi samxreTis mimarTulebiT 192 km/sT siCqariT, meore – aRmosavleTis mimarTulebiT 256 km/sT siCqariT. ra manZilze iqnebian erTmaneTisagan TviTmfrinavebi 3 saaTis Semdeg? 48 ori gemi erTdroulad gavida navsadguridan: erTi CrdiloeTiT, meore aRmosavleTiT. ori saaTis Semdeg maT Soris manZili 60 km aRmoCnda. ipoveT TiToeuli gemis siCqare, Tu cnobilia, rom erTis siCqare 6 km/sT-iT metia meorisaze. 49 klubis darbazSi 320 adgilia. imis Semdeg, rac TiToeul rigSi adgilebis ricxvi 4-iT gaadides da kidev erTi rigi daumates, darbazSi 420 adgili gaxda. ramdeni rigia axla klubis darbazSi? 50 mamam 36 vaSli xuT Svils gauyo. naxevari vaJebs misca, maT igi Tanasworad gainawiles. meore naxevari qaliSvilebs ergoT. ganawileba maT Sorisac Tanabrad moxda. aRmoCnda, rom TiToeulma qaliSvilma miiRo 3 vaSliT meti, vidre TiToeulma vaJma. ramdeni vaJi hyavda mamas? 51 oTxi dRis erTad muSaobiT sxvadasxva simZlavris orma traqtorma sakolmeurneo farTobis 2/3 nawili moxna. ramden dReSi moxnavda mTel farTobs TiToeuli traqtori cal – calke, Tu pirvel traqtors SeuZlia mTeli farTobis 5 dRiT swrafad moxvna, vidre meores? 52 erTi da imave procentuli maCvenebliT fasebis orjer daklebis Semdeg fotoaparatis fasi 90 laridan 72,2 laramde daeca. ramdeni procentiT klebulobda TiToeul SemTxvevaSi fotoaparatis fasi? 53 qalaqis mosaxleoba 2 wlis ganmavlobaSi 800000 kacidan 832320 kacamde gaizarda. ipoveT mosaxleobis zrdis yovelwliuri saSualo procenti. 54 fexburTSi moswavleTa Soris qalaqis pirvelobaze 66 matCi Catarda. ramdeni gundi monawileobda gaTamaSebaSi, Tu cnobilia, rom TiToeulma gundma danarCen gundebTan mxolod TiTo matCi Caatara? 55 amozneqil mravalkuTxedSi yvela SesaZlo diagonalebis ricxvi 54-ia. ramdeni gverdi aqvs mravalkuTxeds? 56 gamosaSvebi klasis moswavleebma erTmaneTs samaxsovrod suvenirebi dauriges. ramdeni moswavle yofila klasSi, Tu gacvla-gamocvlisaTvis saWiroa 870 suveniri? 53
Page 3: nana jafariZe maia wilosani nani
Page 6 and 7: IV Tavi . . . . . . . . . . . . . .
Page 8 and 9: 6 rogor visargebloT wigniT wignze m
Page 10 and 11: I Tavi 8 f funqciaa h ar aris funqc
Page 12 and 13: I Tavi gasaxseneblad! p(A) = m n ,
Page 14 and 15: I Tavi -4 12 4 a) savarjiSoebi: 1 r
Page 16 and 17: I Tavi 14 4) rodis moawyves turiste
Page 18 and 19: I Tavi 16 2 amovicnoT wrfivi funqci
Page 20 and 21: I Tavi 18 SeavseT gamotovebuli adgi
Page 22 and 23: I Tavi 20 proeqti: gazomvebidan fun
Page 24 and 25: I Tavi 22 y 10 -3 -2 -1 0 1 2 3 9 8
Page 26 and 27: I Tavi 24 15% 1,5 < n ≤ 2 20% 1 <
Page 28 and 29: I Tavi 26 nax. 1 kvadratul gantoleb
Page 30 and 31: I Tavi 28 3 dawereT kvadratuli gant
Page 32 and 33: I Tavi davazustoT! roca D = 0, kvad
Page 34 and 35: I Tavi 32 amovxsnaT formuliT (3x 2
Page 36 and 37: I Tavi 34 z) 10x 2 −120 + 6x = 98
Page 38 and 39: I Tavi navis sakuTari siCqarea navi
Page 40 and 41: I Tavi 38 6 amovxsnaT jgufuri mecad
Page 42 and 43: I Tavi x 1 da x 2 ricxvebi arian x
Page 44 and 45: I Tavi 42 17 amoxseniT gantoleba: a
Page 46 and 47: I Tavi 44 yuradReba: Tu D=0, maSin,
Page 48 and 49: I Tavi gavixsenoT! x = a, maSin a 2
Page 50 and 51: I Tavi 48 I Tavis damatebiTi savarj
Page 52 and 53: I Tavi 50 K y = x 2 A B -3 -2 -1 K
Page 56 and 57: I Tavi narevSi gaxsnili nivTierebis
Page 58: 56 I TavSi Seswavlili masalis mokle

I Tavi

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